The Effect of
Inspection Intervals

Consider a little known
airline, Odyssey Air, that uses inflatable life vests manufactured by
ACME Life Vest Company aboard its commercial aircraft. Odyssey Air wants
to study and understand the effect of different inspection intervals for
these life vests. The vests are stored until they are required for use.
Therefore, failures remain dormant until the system is needed or until
failed vests are discovered during scheduled inspections. Scheduled
inspections involve testing all vests on the aircraft. Vests found
failed are discarded and replaced with new vests (thus resulting in a
mix of vests of different ages aboard the aircraft). Odyssey Air is
contemplating different inspection intervals for these life vests. They
wish to study the effect of inspections performed annually, every two
years and every three years.

Setup

Past replacement data was utilized and a dormant failure distribution
for these vests was obtained with the following properties:

Weibull life
distribution

Beta = 2.55

Eta = 6.89 years

One way to approach
this using BlockSim is to
set up a single block with the given dormant failure distribution.
Figure 1 shows the analysis set up in BlockSim.

If a vest is found
failed, it is replaced; thus, a corrective action needs to be set for
the block. In addition, one can assume instantaneous replacement (i.e.
zero duration) since the time to perform the inspection and replace the
vest is not of interest for this analysis.Furthermore, and since the
vests are replaced with new ones, a
restoration factor equal to 1 can be assumed.

The corrective action
is not initiated until the vest is found failed. Thus, the corrective
action will be based upon an inspection. In BlockSim, the "Upon
Inspection" option needs to be selected.
In addition,for
annual inspections, the inspection would be once a year, and so forth.

Once the
problem has been set up, simulation is utilized to see the effect of the
inspection intervals. In this case, the
instantaneous or point availability, A(t), is what is of interest.
Within the context of this example, this will represent the probability
that a vest will be operational (non-failed) at a specific point in
time.

Annual Inspection

Figure 2 shows A(t) when utilizing annual inspections. As can be seen on
the plot, A(t) goes to 1 after each inspection, implying that 100% of
the vests are in a non-failed state after the inspection.

Figure 2: Availability for 1 year inspection

From the plot, it can
be seen that after 1.5 years, A(t) is approximately 98%. This implies
that 2% of the vests on the aircraft are in a failed state at that point
in time. Furthermore, the following can be noted:

The percent
non-failed decreases after each inspection.

The rate of decrease
of A(t) keeps on increasing after each subsequent inspection (since
non-failed vests are not replaced and the population ages) until a
periodic reversal point is reached at which most vests are replaced with
newer ones, thus yielding a younger population.

Figures 3 and 4 repeat
the analysis using two and three year inspection plans.

Figure 3: Availability for 2 year inspection

Figure 4: Availability for 3 year inspection

As can be
seen from the plots, the availability of the life vests changes
dramatically as the interval of inspection increases. Based on the
selected inspection intervals, Odyssey Air can now select the inspection
interval for the life vests that meets their required goals.